## 抄録

In this article, we study the Ising vectors in the vertex operator algebra V^{+}∧ associated with the Leech lattice ∧. The main result is a characterization of the Ising vectors in V^{+}∧. We show that for any Ising vector e in V^{+}∧, there is a sublattice E ≅ √2E_{8} of ∧ such that e ∈ V^{+}E . Some properties about their corresponding τ -involutions in the moonshine vertex operator algebra V are also discussed.We show that there is no Ising vector of σ- type in V. Moreover, we compute the centralizer CAutV(z, τe) for any Ising vector e ∈ V^{+}∧, where z is a 2B element in AutV which fixes V^{+}∧. On the basis of this result, we also obtain an explanation for the 1A case of an observation by Glauberman-Norton (2001), which describes some mysterious relations between the centralizer of z and some 2A elements commuting z in the Monster and the Weyl groups of certain sublattices of the root lattice of type E_{8}.

本文言語 | English |
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論文番号 | rnm132 |

ジャーナル | International Mathematics Research Notices |

巻 | 2007 |

DOI | |

出版ステータス | Published - 2007 12月 1 |

外部発表 | はい |

## ASJC Scopus subject areas

- 数学 (全般)

## フィンガープリント

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